Persistent Homology Live

Draw points, watch topology emerge and die
Point cloud (click to add points)
Persistence diagram H₀ (dots) H₁ (circles)
Persistence barcodes — horizontal bars = feature lifetimes
H₀ = connected components (dots), H₁ = loops (circles). Features born at ε_birth, die at ε_death. Long bars = topologically significant features.